Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives

References

• Atkinson , A. C. 1982 . The Simulation of Generalized Inverse Gaussian and Hyperbolic Random Variables . SIAM Journal on Scientific and Statistical Computing , 3 : 502 – 515 .
   Web of Science ®Google Scholar
• Barndorff-Nielsen , O. and Blaesild , P. 1983 . Hyperbolic Distributions , New York : John Wiley & Sons .
   Google Scholar
• Bartholomew , D. J. 1961 . Ordered Tests in the Analysis of Variance . Biometrika , 48 : 325 – 332 .
   Web of Science ®Google Scholar
• Bartlett , M. S. 1937 . Properties of Sufficiency and Statistical Tests . Proceedings of the Royal Society, Series A , 160 : 268 – 282 .
   Google Scholar
• Bechhofer , R. E. and Dunnett , C. W. 1982 . Multiple Comparisons for Orthogonal Contrasts: Examples and Tables . Technometrics , 24 : 213 – 222 .
   Web of Science ®Google Scholar
• Boos , D. D. and Brownie , C. 1989 . Bootstrap Methods for Testing Homogeneity of Variances . Technometrics , 31 : 69 – 82 .
   Web of Science ®Google Scholar
• Boswell , M. T. and Brunk , H. D. 1969 . Distribution of Likelihood Ratio in Testing Against Trend . Annals of Mathematical Statistics , 40 : 371 – 380 .
   Google Scholar
• Box , G. E.P. 1953 . Nonnormality and Tests on Variances . Biometrika , 36 : 318 – 335 .
   Google Scholar
• Brown , M. B. and Forsythe , A. B. 1974 . Robust Tests for Equality of Variances . Journal of the American Statistical Association , 69 : 364 – 367 .
   Web of Science ®Google Scholar
• Brunk , H. D. 1955 . Maximum Likelihood Estimates of Monotone Parameters . Annals of Mathematical Statistics , 26 : 607 – 616 .
   Google Scholar
• Cabrera , J. and McDougall , A. 2002 . Statistical Consulting , New York : Springer .
   Google Scholar
• Carroll , R. J. and Schneider , H. 1985 . A Note on Levene's Tests for Equality of Variances . Statistics and Probability Letters , 3 : 191 – 194 .
   Web of Science ®Google Scholar
• Clark-Carter , D. 1997 . Doing Quantitative Psychological Research , East Sussex : Psychology Press .
   Google Scholar
• Cochran , W. G. 1941 . The Distribution of the Largest of a Set of Estimated Variances as a Fraction of their Total . Annals of Eugenics , 11 : 47 – 52 .
   Google Scholar
• Conover , W. J. , Johnson , M. E. and Johnson , M. M. 1981 . A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data . Technometrics , 23 : 351 – 361 .
   Web of Science ®Google Scholar
• Cunningham , G. R. , Matsumoto , A. M. and Swerdloff , R. 2004 . Low Testosterone and Men's Health . Journal of Clinical Endocrinology & Metabolism , 89 ( 5 ) http://jcem.endojournals.org/cgi/content/full/jcem;89/5/0
   Google Scholar
• Descartes , R. 1637 . Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences , Fairfield, IA : 1st World Library .
   Google Scholar
• Efron , B. 1979 . Bootstrap Methods: Another Look at the Jackknife . Annals of Statistics , 7 : 1 – 26 .
   Web of Science ®Google Scholar
• Fisher , R. A. 1932 . Statistical Methods for Research Workers , Edinburgh : Oliver and Boyd .
   Google Scholar
• Fujino , Y. 1979 . Tests for the Homogeneity of Variances for Ordered Alternatives . Biometrika , 66 : 133 – 139 .
   Web of Science ®Google Scholar
• Gastwirth , J. L. 1982 . Statistical Properties of a Measure of Tax Assessment Uniformity . Journal of Statistical Planning and Inference , 6 : 1 – 12 .
   Web of Science ®Google Scholar
• Gastwirth , J. L. , Gel , Y. R. and Miao , W. 2010 . The Impact of Levene's Test for Equality of Variances on Statistical Theory and Practice . Statistical Science , to appear. http://www.imstat.org/sts/future_papers.html
   Google Scholar
• Griffith , D. A. 2002 . The Geographic Distribution of Soil Lead Concentration: Description and Concerns . URISA Journal , 14 : 5 – 15 .
   Google Scholar
• Grimmett , G. R. and Stirzaker , D. R. 2001 . Probability and Random Processes , New York : Oxford University Press .
   Google Scholar
• Gupta , A. K. , Harrar , S. W. and Pardo , L. 2007 . On Testing Homogeneity of Variances for Nonnormal Models Using Entropy . Statistical Methods and Applications , 16 : 245 – 261 .
   Google Scholar
• Hallin , M. and Paindaveine , D. 2008 . A General Method for Constructing Pseudo-Gaussian Tests . Journal of the Japan Statistical Society , 38 : 27 – 39 .
   Google Scholar
• Hines , W. G.S. and O'Hara Hines , R. J. 2000 . Increased Power with Modified Forms of the Levene (med) Test for Heterogeneity of Variance . Biometrics , 56 : 451 – 454 .
   PubMed Web of Science ®Google Scholar
• Hogg , R. V. 1961 . On the Resolution of Statistical Hypotheses . Journal of the American Statistical Association , 56 : 978 – 989 .
   Web of Science ®Google Scholar
• Hogg , R. V. 1962 . Iterated Tests of the Equality of Several Distributions . Journal of the American Statistical Association , 57 : 579 – 585 .
   Web of Science ®Google Scholar
• Hogg , R. V. and Tanis , E. A. 1963 . An Iterated Procedure for Testing the Equality of Several Exponential Distributions . Journal of the American Statistical Association , 58 : 435 – 443 .
   Web of Science ®Google Scholar
• Hu , F. and Rosenberger , W. F. 2006 . The Theory of Response-Adaptive Randomization in Clinical Trials , Hoboken, NJ : John Wiley & Sons .
   Google Scholar
• Hui , W. , Gel , Y. R. and Gastwirth , J. L. 2008 . lawstat: An R Package for Law, Public Policy and Biostatistics . Journal of Statistical Software , 28 ( 3 ) http://www.jstatsoft.org/v28/i03/paper
   PubMedGoogle Scholar
• Keyes , T. K. and Levy , M. S. 1997 . Analysis of Levene's Test Under Design Imbalance . Journal of Educational and Behavioral Statistics , 22 : 845 – 858 .
   Google Scholar
• Le , C. T. 1994 . Some Tests for Linear Trend of Variances . Communications in Statistics: Theory and Methods , 23 : 2269 – 2283 .
   Web of Science ®Google Scholar
• Lehmann , E. L. 1998 . Elements of Large-Sample Theory , New York : Springer .
   Google Scholar
• Levene , H. 1960 . “ Robust Testes for Equality of Variances ” . In Contributions to Probability and Statistics , Edited by: Olkin , I. 278 – 292 . Palo Alto, CA : Stanford University Press .
   Google Scholar
• Lim , T. S. and Loh , W. Y. 1996 . A Comparison of Tests of Equality of Variances . Computational Statistics and Data Analysis , 22 : 287 – 301 .
   Web of Science ®Google Scholar
• Liptak , T. 1958 . On the Combination of Independent Tests . Magyar Tudomanyos Akademia Matematikai Kutato Intezetenek Kozlemenysi , 3 : 171 – 197 .
   Google Scholar
• Manoukian , E. B. , Maurais , J. and Ouimet , R. 1986 . Exact Critical Values of Bartlett's Test of Homogeneity of Variances for Unequal Sample Sizes for Two Populations and Power of the Test . Metrika , 33 : 275 – 289 .
   Google Scholar
• McDermott , M. P. and Mudholkar , G. S. 1993 . A Simple Approach to Testing Homogeneity of Orderconstrained Means . Journal of the American Statistical Association , 88 : 1371 – 1379 .
   Google Scholar
• Miller , R. G. Jr. 1968 . Jacknifing Variances . Annals of Mathematical Statistics , 39 : 567 – 582 .
   Google Scholar
• Mitchell , B. R. 1981 . To the Editor . Toxicology and Applied Pharmacology , 58 : 333
   Google Scholar
• Mudholkar , G. S. and George , E. O. 1979 . “ The Logit Statistic for Combining Probabilities – An Overview ” . In Optimizing Methods in Statistics , Edited by: Rustagi , J. S. 345 – 365 . New York : Academic Press .
   Google Scholar
• Mudholkar , G. S. and McDermott , M. P. 1989 . A Class of Tests for Equality of Ordered Means . Biometrika , 76 : 161 – 168 .
   Web of Science ®Google Scholar
• Mudholkar , G. S. , McDermott , M. P. and Aumont , J. 1993 . Testing Homogeneity of Ordered Variances . Metrika , 40 : 271 – 281 .
   Google Scholar
• Mudholkar , G. S. , McDermott , M. P. and Mudholkar , A. 1995 . Robust Finite-intersection Tests for Homogeneity of Ordered Variances . Journal of Statistical Planning and Inference , 43 : 185 – 195 .
   Google Scholar
• Natarajan , R. , Mudholkar , G. S. and McDermott , M. P. 2005 . Order Restricted Inference for the Scale-like Inverse Gaussian Parameters . Journal of Statistical Planning and Inference , 127 : 229 – 236 .
   Web of Science ®Google Scholar
• Nelson , W. B. 1972 . A Short Life Test for Comparing a Sample with Previous Accelerated Test Results . Technometrics , 14 : 175 – 185 .
   Google Scholar
• Neuhäuser , M. 2007 . A Comparative Study of Nonparametric Two-sample Tests after Levene's Transformation . Journal of Statistical Computation and Simulation , 77 : 517 – 526 .
   Web of Science ®Google Scholar
• Neuhäuser , M. and Hothorn , L. A. 2000 . Location-scale and Scale Trend Tests Based on Levene's Transformation . Computational Statistics and Data Analysis , 33 : 189 – 200 .
   Google Scholar
• O'Brien , R. G. 1978 . Robust Techniques for Testing Heterogeneity of Variance Effects in Factorial Designs . Psychometrika , 43 : 327 – 344 .
   Web of Science ®Google Scholar
• O'Neil , M. E. and Mathews , K. L. 2000 . A Weighted Least Squares Approach to Levene's Test of Homogeneity of Variance . Australian and New Zealand Journal of Statistics , 42 : 81 – 100 .
   Google Scholar
• Olkin , I. and Tomsky , J. L. 1981 . A New Class of Multivariate Tests Based on the Union-intersection Principle . Annals of Statistics , 9 : 792 – 802 .
   Google Scholar
• Roy , S. N. 1953 . On a Heuristic Method of Test construction and its use in Multivariate Analysis . Annals of Mathematical Statistics , 24 : 220 – 238 .
   Google Scholar
• Tippett , L. H. 1931 . The Methods of Statistics , London : Williams and Norgate .
   Google Scholar
• Underwood , A. J. 1997 . Experiments in Ecology: Their Logical Design and Interpretation Using Analysis of Variance , Cambridge : Cambridge University Press .
   Google Scholar
• Vincent , S. E. 1961 . A Test of Homogeneity for Ordered Variances . Journal of the Royal Statistical Society, Series B , 23 : 195 – 206 .
   Google Scholar
• Zhang , S. Fourteen Homogeneity of Variance Tests: When and How to Use Them . Paper Presented at the Annual Meeting of the American Educational Research Association . April 1998 , San Diego, California. pp. 13 – 17 .
   Google Scholar